function [mssim, ssim_map] = ssim(img1, img2, K, window, L)

%
%Input : (1) img1: the first image being compared
%        (2) img2: the second image being compared
%        (3) K: constants in the SSIM index formula (see the above
%            reference). defualt value: K = [0.01 0.03]
%        (4) window: local window for statistics (see the above
%            reference). default widnow is Gaussian given by
%            window = fspecial('gaussian', 11, 1.5);
%        (5) L: dynamic range of the images. default: L = 255
%
%Output: (1) mssim: the mean SSIM index value between 2 images.
%            If one of the images being compared is regarded as
%            perfect quality, then mssim can be considered as the
%            quality measure of the other image.
%            If img1 = img2, then mssim = 1.
%        (2) ssim_map: the SSIM index map of the test image. The map
%            has a smaller size than the input images. The actual size
%            depends on the window size and the downsampling factor.
%
% ?sic Usage:
%   Given 2 test images img1 and img2, whose dynamic range is 0-255
%
%   [mssim, ssim_map] = ssim(img1, img2);
%
% ?vanced Usage:
%   User defined parameters. For example
%
%   K = [0.05 0.05];
%   window = ones(8);
%   L = 100;
%   [mssim, ssim_map] = ssim(img1, img2, K, window, L);
%
%Visualize the results:
%
%   mssim                        %Gives the mssim value
%   imshow(max(0, ssim_map).^4)  %Shows the SSIM index map
%========================================================================

if (nargin < 2 | nargin > 5)
   ssim_index = -Inf;
   ssim_map = -Inf;
   return;
end
if (size(img1) ~= size(img2))
   ssim_index = -Inf;
   ssim_map = -Inf;
   return;
end
[M N] = size(img1);
if (nargin == 2)
   if ((M < 11) | (N < 11))
    ssim_index = -Inf;
    ssim_map = -Inf;
      return
   end
   window = fspecial('gaussian', 11, 1.5); %
   K(1) = 0.01;     % default settings
   K(2) = 0.03;     %
   L = 255;                                     %
end
if (nargin == 3)
   if ((M < 11) | (N < 11))
    ssim_index = -Inf;
    ssim_map = -Inf;
      return
   end
   window = fspecial('gaussian', 11, 1.5);
   L = 255;
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
     ssim_index = -Inf;
     ssim_map = -Inf;
     return;
      end
   else
    ssim_index = -Inf;
    ssim_map = -Inf;
    return;
   end
end
if (nargin == 4)
   [H W] = size(window);
   if ((H*W) < 4 | (H > M) | (W > N))
    ssim_index = -Inf;
    ssim_map = -Inf;
      return
   end
   L = 255;
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
     ssim_index = -Inf;
     ssim_map = -Inf;
     return;
      end
   else
    ssim_index = -Inf;
    ssim_map = -Inf;
    return;
   end
end
if (nargin == 5)
   [H W] = size(window);
   if ((H*W) < 4 | (H > M) | (W > N))
    ssim_index = -Inf;
    ssim_map = -Inf;
      return
   end
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
     ssim_index = -Inf;
     ssim_map = -Inf;
     return;
      end
   else
    ssim_index = -Inf;
    ssim_map = -Inf;
    return;
   end
end

img1 = double(img1);
img2 = double(img2);
% automatic downsampling
f = max(1,round(min(M,N)/256));
%downsampling by f
%use a simple low-pass filter
if(f>1)
    lpf = ones(f,f);
    lpf = lpf/sum(lpf(:));
    img1 = imfilter(img1,lpf,'symmetric','same');
    img2 = imfilter(img2,lpf,'symmetric','same');
    img1 = img1(1:f:end,1:f:end);
    img2 = img2(1:f:end,1:f:end);
end
C1 = (K(1)*L)^2;
C2 = (K(2)*L)^2;
window = window/sum(sum(window));
mu1   = filter2(window, img1, 'valid');
mu2   = filter2(window, img2, 'valid');
mu1_sq = mu1.*mu1;
mu2_sq = mu2.*mu2;
mu1_mu2 = mu1.*mu2;
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;
if (C1 > 0 & C2 > 0)
   ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2));
else
   numerator1 = 2*mu1_mu2 + C1;
   numerator2 = 2*sigma12 + C2;
denominator1 = mu1_sq + mu2_sq + C1;
   denominator2 = sigma1_sq + sigma2_sq + C2;
   ssim_map = ones(size(mu1));
   index = (denominator1.*denominator2 > 0);
   ssim_map(index) = (numerator1(index).*numerator2(index))./(denominator1(index).*denominator2(index));
   index = (denominator1 ~= 0) & (denominator2 == 0);
   ssim_map(index) = numerator1(index)./denominator1(index);
end
mssim = mean2(ssim_map);